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How does GPS work?

The genius of longitude

For every 15° that one travels eastward, the local time moves one hour ahead. Similarly, travelling West, the local time moves back one hour for every 15° of longitude.
Therefore, if we know the local times at two points on Earth, we can use the difference between them to calculate how far apart those places are in longitude, east or west.
Although accurate pendulum clocks existed in the 17th century, the motions of a ship and changes in humidity and temperature would prevent such a clock from keeping accurate time at sea.

In 1714 the British parliament offered a reward of £20,000 (equivalent to about US$1 million today) to anyone who could find a way to sail from Great Britain to the West Indies without losing their Longitude beyond half-a-degree (2 minutes). And surprise, surprise; someone did.

Eventually. Though for many years people believed the problem simply could not be solved. The phrase 'finding the longitude' even came to mean behaving like a lunatic.

The longitude problem was eventually solved by John Harrison, a carpenter with little formal education. Through mechanical insight, talent and sheer determination.

After decades striving to design a clock that met the required accuracy for the prize, Harrison’s son (he was himself an old man by now) sailed with his father’s watch from England to Barbados. On arrival the watch's error was computed to be 39.2 seconds over a voyage of 47 days.

Harrison then had to battle for recognition and his rightful prize against a scientific and academic establishment who were reluctant to accept that someone outside their circle could achieve such a feat. After finally gathering the support of King George II himself, Harrison got some of the £20,000 – and more importantly the credit - due to him in 1773.

In the meantime, Captain Cook had used a version of Harrison’s clock on a 3 year voyage that covered the Tropics and the Antarctic. Harrison’s clock’s daily rate never exceeded 8 seconds (or a distance of 2 nautical miles at the equator). Cook called it “our faithful guide through all the vicissitudes of climates.”